It comes as pro- and anti-government protesters take part in rival rallies in the capital, Caracas.
Leopoldo Lopez, who is wanted on charges of inciting violence, had said he would lead the anti-government march before handing himself in to the authorities.
Tensions have been running high in the deeply polarized country; at least three people have died in clashes.
The three – two anti-government protesters and one government supporter – died of bullet wounds sustained during demonstrations last Wednesday.
Participants in a protest in the eastern city of Carupano said another student was killed when he was run over by a car during a march on Monday night.
Leopoldo Lopez got into an armored vehicle after giving a speech to an opposition rally in Caracas to give himself in on Tuesday, according to Reuters.
Ahead of the rallies, Caracas Mayor Jorge Rodriguez warned that he had not authorized Tuesday’s opposition march.
Police and members of the National Guard are out in force. Opposition activists have accused them of trying to prevent them from attending the anti-government rally.
The anti-government demonstration was called by Leopoldo Lopez, leader of the opposition Popular Will party and former mayor of Chacao district in eastern Caracas.
Earlier, Leopoldo Lopez urged his supporters to join the march but asked them to stop short of the Interior Ministry, which is located in a pro-government area of Caracas and where he was planning to hand in a petition.
“I will walk alone. I won’t put any Venezuelan lives at risk. Go Venezuela!” he wrote on Twitter.
In a video statement released on Sunday, Leopoldo Lopez said he had not committed any crime and insisted allegations that he had incited violence were untrue.
Leopoldo Lopez also promised to hand himself in at the end of Tuesday’s march.
“If there is a decision to legally throw me in jail, I’ll submit myself to this persecution,” he said.
Thousands of people have gathered in the east of Caracas in support of Leopoldo Lopez.
He had been expected to join the march and lead it towards the Interior Ministry.
The US state department earlier denied that it was helping to organize the anti-government protests.
“The allegation that the United States is helping to organize protesters in Venezuela is baseless and false,” spokeswoman Jennifer Psaki said.
The statement came a day after Venezuela announced it would expel three US diplomats for allegedly meeting students who had been leading marches.
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